Question

Which of the following statements is/are true?

• A. The general term in the expansion of $\left(x^2-y\right)^6$ is ${ }^6 C$ $x^{10-2 r} y^r(-1)^r$
• B. The general term in the expansion of $\left(x^2-y x\right)^{12}, x \neq 0$ is ${ }^{12} C_r(-1)^r x^{24-r} y^r$
• C. Both (a) and (b) are true
• D. Both (a) and (b) are false

Answer 1

Answer: (B)

(a) The general term of $\left(x^2-y\right)^6$ is
$T_{r+1} ={ }^6 C_r\left(x^2\right)^{6-r}(-y)^r={ }^6 C_r x^{12-2 r}(-1)^r y^r$
$={ }^6 C_r x^{12=2 r} y^r(-1)^r$
(b) The general term of $\left(x^2-y x\right)^{12}$ is
$T_{r+1} ={ }^{12} C_r\left(x^2\right)^{12-r}(-y x)^r$
$ ={ }^{12} C_r x^{24-2 r}(-1)^r y^r x^r$
$ ={ }^{12} C_r(-1)^r x^{24-2 r+r} y^r$
$ -{ }^{12} C_r(-1)^r x^{24-r} y^r$
So, only (b) is correct.